We used 3.1 million spectroscopically labelled sources from the Sloan Digital Sky Survey (SDSS) to train an optimised random forest classifier using photometry from the SDSS and the Widefield Infrared Survey Explorer. We applied this machine learning model to 111 million previously unlabelled sources from the SDSS photometric catalogue which did not have existing spectroscopic observations. Our new catalogue contains 50.4 million galaxies, 2.1 million quasars, and 58.8 million stars. We provide individual classification probabilities for each source, with 6.7 million galaxies (13%), 0.33 million quasars (15%), and 41.3 million stars (70%) having classification probabilities greater than 0.99; and 35.1 million galaxies (70%), 0.72 million quasars (34%), and 54.7 million stars (93%) having classification probabilities greater than 0.9. Precision, Recall, and F 1 score were determined as a function of selected features and magnitude error. We investigate the effect of class imbalance on our machine learning model and discuss the implications of transfer learning for populations of sources at fainter magnitudes than the training set. We used a non-linear dimension reduction technique, Uniform Manifold Approximation and Projection, in unsupervised, semi-supervised, and fully-supervised schemes to visualise the separation of galaxies, quasars, and stars in a two-dimensional space. When applying this algorithm to the 111 million sources without spectra, it is in strong agreement with the class labels applied by our random forest model.